Preheat the oven to 450ºF. Put the oil in a large oven safe skillet and heat on medium-high. When the oil shimmers but before it smokes, arrange the sprouts in one layer, cut side down. Add the garlic and season with salt and pepper.
Cook, undisturbed, until the sprouts begin to brown, about 5 minutes. Move the pan to the oven and cook, shaking the pan occasionally, until the sprouts are very brown and tender, about 30 minutes.
Drizzle with the vinegar and adjust seasoning as necessary. Stir and serve.
Note: I recommend removing the garlic cloves before serving. They're left whole and they cook down to a delicious, mellow garlic flavor, but for my family it was too much. You can leave them in or set them aside and spread them on crusty french bread for a tasty side also.Adapted from How to Cook Everything